Higher spin constraints and the super $( W_{\infty\over 2}\oplus W_{{1+\infty}\over 2})$ algebra in the super eigenvalue model

TL;DR

This paper demonstrates that the partition function of a super eigenvalue model obeys an infinite set of constraints linked to a super W-algebra, extending the understanding of symmetries in such models.

Contribution

It establishes the connection between super eigenvalue models and the super W-infinity algebra, including the derivation of constraints and their relation to super Virasoro constraints.

Findings

Partition function satisfies infinite super W-algebra constraints.

Constraints include half of the bosonic generators of the super W-infinity algebra.

Results are valid for finite N.

Abstract

We show that the partition function of the super eigenvalue model satisfies an infinite set of constraints with even spins $s=4,6,\cdots,\infty$. These constraints are associated with half of the bosonic generators of the super $\left( W_{\infty \over 2}\oplus W_{{1+\infty}\over 2}\right)$ algebra. The simplest constraint $(s=4)$ is shown to be reducible to the super Virasoro constraints, previously used to construct the model. All results hold for finite $N$.